Measuring Decline

Introduction

Data

Data on Property Taxes, Elementary Education Expenditure, Private Industry and Total GDP at the county, commuting zone, state, and national levels.

Relationships Between the Variables

Elem. Ed. Exp. and Priv. Ind. GDP

Levels

At a state level, we see that elementary ed expenditure does somewhat follow the shape of private industry GDP, with significant exceptions (ex. Michigan).

Growth Rates

Elem. Ed. Exp. and Property Tax

Levels

Elementary ed expenditure follows the behaviour of property taxes in most states, with very few exceptions…

FDs

Property Tax and Priv. Ind. GDP

Levels

Property taxes collected do also seem to grow in line with private industry GDP (all in real values) with a few notable exceptions: Delaware, Idaho, Indiana, Kansas, Minnesota, North Dakota.

FDs

Defining Decline

What would be great is to be able to econometrically test when a county is “declining.” In the first step, it would be good to identify when a county is declining overall (GDP, poverty, etc) but ideally eventually apply this to the education outcome. My hope is that being able to identify counties that are “declining” we can either use this variable as a covariate or as a central point of analysis. The below analysis looks at state-level variables as a first step (mainly to aid in visual comparison and plotting). This has now been expanded to county and commuting zones levels.

Some current options:

• Simple time trends

• Exhibit national or state-level GDP growth as global common factor; counties with negative factor loadings might arguably exhibit decline (_)

• Jennie’s suggestion:

  • plot county- , CZ, or state-level deviations from a national trend

Education

Deviation from T0

One way to look at this descriptively is to look at the national, state and county-level trends. Here the “trend” is simply the difference between expenditure per pupil at the relevant level and expenditure per pupil in the first available observation as represented here: https://www.princeton.edu/~erossi/DTNLC.pdf. (Note: this measure is imperfect for many reasons).

States

CZs

delta_log_real_Elem_Educ_Total_Exp_pp

delta_ma3_log_real_Elem_Educ_Total_Exp_pp

Counties

delta_log_real_Elem_Educ_Total_Exp_pp

delta_ma3_log_real_Elem_Educ_Total_Exp_pp

Trends

Trend in log Elementary Education Expenditure (growth rate). The below plots show the coefficient estimate on the time-step variable in the trend equation. In the first panel I include no additional controls but in the latter two panels I include the state and national level growth rates as controls.

# Coefficient on state and national level trends
county_ed_sensitivities %>% 
  pivot_longer(cols = contains("sensitivity")) %>% 
  ggplot() +
  geom_histogram(aes(x = value, fill = name), bins = 100, position = "identity") +
  scale_fill_brewer(palette = "Set2")

plot_usmap(data = mute_outliers(county_ed_sensitivities, "sensitivity_natl"), values = "var_muted", regions = "counties", col = "gray90", linewidth = 0.01, exclude = c("AK", "HI")) +
  scale_fill_gradient2(na.value = "grey98", midpoint = 0) +
  #scale_fill_distiller(colours=c(bl,"white", re), name = "", direction = 1, na.value = "gray90", limits = c(-1, 1)) +
   theme(panel.background = element_rect(color = "white", fill = "white"),
       plot.title = element_text(face = "bold"), legend.background=element_blank()) +
    labs(title = "County-level Sensitivity to National Trend in Elem. Ed. Exp. pp") +
  ggplot2::geom_sf(data = dat, colour = "blue", fill = NA, linewidth = 0.1)

plot_usmap(data = mute_outliers(county_ed_sensitivities, "sensitivity_state"), values = "var_muted", regions = "counties", col = "gray90", linewidth = 0.01, exclude = c("AK", "HI")) +
 scale_fill_gradient2(na.value = "grey98", midpoint = 0) +
  #scale_fill_distiller(colours=c(bl,"white", re), name = "", direction = 1, na.value = "gray90", limits = c(-1, 1)) +
    theme(panel.background = element_rect(color = "white", fill = "white"),
        plot.title = element_text(face = "bold"), legend.background=element_blank()) +
    labs(title = "County-level Sensitivity to State Trend in Elem. Ed. Exp. pp") +
   ggplot2::geom_sf(data = dat, colour = "blue", fill = NA, linewidth = 0.1)

Growth Rates

States

Commuting Zones

Counties

Outliers

Negative

Positive

GDPPC

Trends

Trend in log Real GDP (growth rate). The below plots show the coefficient estimate on the time-step variable in the trend equation. In the first panel I include no additional controls but in the latter two panels I include the state and national level growth rates as controls.

Outliers

Negative

Positive

Progress on Jennie’s Suggestion

1. National data on GDP, UER, (and poverty)

2. State data on GDP, UER, and poverty

3. Extract trends of state and national data

4. Deviations at county level from national and state-level trends

5. Plot deviations

6. Saturation to find structural breaks in these deviations

Result: UE, GDP, and Poverty gaps

7. PCA on those three gaps

8. Retain index from PCA

9. Step break in index

10. Line up with any notable events?

11. Place “gaps” in a panel structure for break detection

12. Autocorrelation plot to test no residual autocorrelation in model above with PCA indices.

Supplementary Materials

Cointegration testing

Suggestions from Jennie:

Engle-Granger Test - bivariate scenario

Johanson Test - multivariate setting [GDP, Property Taxes, Ed. Spending]

Autocorrelation

First-differences

• Autocorrelation (Education only) (X)

• Correlation plots (X)

• Cross-correlation plot of Education and GDP (X)

• Are GDP and Education Expenditure cointegrating (or do they exhibit a decoupling?) (_)

Autocorrelation

First-differences

Correlation Plots (Education and GDP)

Cross-correlation of Educ Exp and Priv. Industry GDP

Autocorrelations of series 'X', by lag

   -10     -9     -8     -7     -6     -5     -4     -3     -2     -1      0 
-0.051 -0.019 -0.225 -0.376 -0.146 -0.043  0.316  0.632  0.555  0.293  0.001 
     1      2      3      4      5      6      7      8      9     10 
-0.418 -0.199 -0.196 -0.028  0.230 -0.099 -0.118 -0.016 -0.081 -0.040 

Autocorrelations of series 'X', by lag

   -10     -9     -8     -7     -6     -5     -4     -3     -2     -1      0 
-0.224 -0.172 -0.120  0.009  0.227  0.532  0.439  0.313 -0.038 -0.064  0.087 
     1      2      3      4      5      6      7      8      9     10 
 0.013 -0.068 -0.104 -0.184 -0.154 -0.038 -0.120  0.002 -0.327 -0.170 

Autocorrelations of series 'X', by lag

   -10     -9     -8     -7     -6     -5     -4     -3     -2     -1      0 
-0.373 -0.107 -0.201 -0.145 -0.145 -0.191  0.203  0.343  0.581  0.698  0.237 
     1      2      3      4      5      6      7      8      9     10 
-0.147 -0.061 -0.198 -0.115 -0.235 -0.285 -0.131 -0.256 -0.084 -0.002 

Autocorrelations of series 'X', by lag

   -10     -9     -8     -7     -6     -5     -4     -3     -2     -1      0 
-0.004 -0.036 -0.164 -0.287 -0.272 -0.127  0.036  0.141  0.365  0.557  0.101 
     1      2      3      4      5      6      7      8      9     10 
 0.115  0.171  0.051 -0.189 -0.155 -0.091 -0.201 -0.250 -0.061  0.030 

Autocorrelations of series 'X', by lag

   -10     -9     -8     -7     -6     -5     -4     -3     -2     -1      0 
 0.012  0.012 -0.046  0.041 -0.176  0.032  0.028  0.345  0.239  0.436  0.116 
     1      2      3      4      5      6      7      8      9     10 
 0.000 -0.203 -0.051 -0.068  0.023 -0.325 -0.138 -0.115 -0.067 -0.216 

Autocorrelations of series 'X', by lag

   -10     -9     -8     -7     -6     -5     -4     -3     -2     -1      0 
 0.085 -0.158  0.351 -0.392 -0.041  0.600 -0.462 -0.188  0.156  0.079 -0.018 
     1      2      3      4      5      6      7      8      9     10 
-0.282  0.231  0.100 -0.187  0.053  0.052  0.095  0.014  0.128 -0.062